Thinking About Metal-Metal Quadruple Bonding in Extended NJC Structures: a Hypothetical A2M6E8 Network

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Thinking about metal-metal quadruple bonding in extended www.rsc.org/njc NJC structures: a hypothetical A2M6E8 network

Musiri M. Balakrishnarajan,a Peter Kroll,b Michael J. Bucknuma and Roald Hoﬀmann*a

a Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, NY 14853-1301, USA. E-mail: [email protected] b Institut fu¨r Anorganische Chemie, Rheinisch-Westfa¨lische Technische Hochschule Aachen, Professor-Pirlet-Strasse 1, 52056, Aachen, Germany

Received (in Montpellier, France) 13th September 2003, Accepted 25th November 2003 First published as an Advance Article on the web 19th January 2004

The electronic and structural possibilities of a recently conceived, as-yet unsynthesized, AM6E8 (or A2M6E8) structural type are explored. With A an alkaline earth metal, M a transition metal, and E a main group element, a range of geometries containing M–M pairs with very short separations is feasible. Density functional theory geometry optimizations and an extended Hu¨ckel analysis of the bonding in a representative Ca2W6O8 realization support the qualitative picture of quadruple metal-metal bonding in these hypothetical phases. The MM pairs interact moderately (metallic behavior is anticipated) through linking atoms. Geometry optimizations of a wide range of hypothetical compounds show that the M–M separation in these will be in the range of realistic quadruple metal-metal bonding, 2.20–2.30 A˚ .

The working out of the idea of metal-metal quadruple bonding Another connection may be made to the Cr3Si type (A15 in by F. A. Cotton is certainly one of the prettiest chapters of Strukturberichte). The A2M6 (=M3A=Cr3Si) framework is modern chemistry.1 Can one realize such bonding in extended stuffed with eight E atoms that fill trigonal bypyramidal holes. structures? There are a number of compounds in which short The superconducting Nb3Ge and Nb3Sn phases belong to this metal-metal separations are observed and which reach formal structural family too.9a Our particular choice of atoms A, M, bond orders of three—for instance, RE2ReO5 (RE ¼ rare and E can be thought of as causing bond localization within 2 2 3 4 earth), RE3Re2O9 , Li6Ca2Mn2N6 , Ca6Cr2N6H, NaNb3- the chains formed by the M atoms of the above-mentioned 5a 5b 5c 5d 9b O5F, Ca0.75Nb3O6 , Ca0.95NbO6 , Na0.74Ta3O6 and structures. 6 some others. Here we propose a hypothetical three-dimen- The A2M6E8 structure may also be related to the fluorite sional network that, while apparently not yet made, seems structure type (CaF2). In CaF2 , Ca atoms are arranged in attainable and that should allow moderately localized MM a cubic closest packing (ccp) arrangement, forming a face- quadruple bonds. centered cell with Ca atoms at the origin as well as on the faces of the cube. F atoms occupy all tetrahedral holes. The coordi- nation of Ca is eight, that of F is four. The octahedral intersti- The structure tial sites (in the center of the cell as well as on the edges) are empty. The composition of the conventional cubic unit cell One of us (MJB) recently proposed a new AM6E8 network, of CaF is Ca F .AM E can be derived from CaF in the 7 2 4 8 2 6 8 2 space group Pm3. The network is shown in Fig. 1. The atoms following way: the Ca at the origin is replaced by an A atom. are located as follows: A: 1(a) (0, 0, 0); M: 6(f) (x, 0, 1/2); Then we split every Ca on the faces into an M–M dimer and E: 8(i) (y, y, y). This net may also exist as a centered exchange all F by E atoms. Finally, we fill the octahedral site A2M6E8 variant, with an additional A atom at (1/2, 1/2, 1/2). in the center of the cube with one A. There are several possibilities to relate the proposed A2M6E8 We present these relations to known structural types structure to well-known structural types in solid state chemis- because of their potential utility in the design of a manifold try. The closest connection is to the known Pt3O4 structure and of structures containing dimer pairs. the Pt bronzes and their chalcogenide analogs.8 In these the Pt–Pt bonding is weak (and interesting) and linearly extended, Design, potential realizations, and sample which, as we will see, is a point of contrast to the structures we propose. calculations Putting A ¼ an alkaline earth metal (a lanthanide, actinide or alkali metal would fit as well), M, a transition metal, and E, a main group element from group 15, 16, or 17, we found a large range of viable structures. Viable is in the sense of A–E, A–M falling in the range of normal ionic separations, M–E a typical coordinate covalent distance, and M–M short, in the range of MM multiple bonds. The environment of the MM unit in 2 AM6E8 is clearly approximately that of Re2Cl8 , as Fig. 1 shows. A further exploration began with three representative d4–d4 10.1039/b311231d compounds: Ca2W6O8 , CaNb6Cl8 , and La2Re6N8 . When

DOI: Fig. 1 The proposed A2M6E8 structure. computed within the extended Hu¨ckel (eH) method, the ﬁrst

This journal is Q The Royal Society of Chemistry and the New. J. Chem., 2004, 28, 185–190 185 Centre National de la Recherche Scientifique 2004 of these had a reasonable gap between three flattish d bonding parameters produced a reasonable correspondence between bands and three d* antibonding ones. The other two com- the eH and DFT band structures of Ca2W6O8 . With the new pounds were metallic as a result of greater dispersion due to parameters, the Ca2W6O8system is metallic in eH. A–E and M–E interactions. When Ca W O was calculated with the Vienna Ab initio 2 6 8 Metal-metal bonding in molecules and the extended structures Simulation Package (VASP) density functional theory (DFT) suite of programs (see details in the Theoretical methods Though the W–W distances computed in our systems are cer- section), permitting complete optimization of all structural tainly short, is there in fact WW quadruple bonding in these parameters (atomic positions and the lattice constant), there structures? Let us look first at a model d4–d4 molecular system, ˚ 12 resulted a short W–W distance of 2.27 A. The distance is W2O8 , computed in the geometry that a dimer unit has in similar to WW quadruple bond separations in molecular Ca2W6O8 . Fig. 2 shows a construction of such a molecule, ˚ ˚ 6 solids, for example, 2.165 A in W2(O2CR)4 and 2.26 A in from two WO4 units. Nothing surprising here—we see the 10 1 Li4W2(CH3)xCl8 xTHF and Li4W2(CH3)8 . expected pattern of s, p, d, d*, p*, s* levels as one goes up There is an important difference between the eH and DFT in energy, perturbed only by an inversion in the order of the results for Ca2W6O8 . In the latter there was substantive den- p* and s* levels. sity of states (DOS) and band crossing at the Fermi level Fig. 3 compares local s, p, and d contributions to the W–W 4 region. The disagreement led us in two directions: (a) explora- crystal orbital overlap population (COOP) in W6O8 and tion with the more reliable DFT code of a wider range of com- Ca2W6O8 . Each was calculated within the eH method, using pounds and (b) a readjustment of the eH parameters, so as to DFT optimized geometries and the adjusted eH parameters potentially match the DFT results. mentioned. s, p and d refer to all combinations that contribute Table 1 shows the compounds we studied, in each case opti- to the COOP, so for instance p is not only dxz(1) dxz(2) but 4 mizing all structural parameters. Most are d systems (88 elec- also includes dxz(1) þ px(2) and px(1) þ px(2) contributions trons in the formula unit), but we also included a range of (where z is the internuclear axis; obviously the analysis is 2.67 compounds with formal electron counts ranging from d restricted to one of the three equivalent W2 sets). 4.67 4 to d . Clearly atom substitutions can be used to tune the W6O8 has a band gap, Ca2W6O8 does not. We see in both electron count and to study its influence on the structure, in compounds well-defined s, p, d, d*, p*, s* regions, though not 4 particular the W–W bond distance. What is remarkable is necessarily in that order. The Fermi level for W6O8 comes how stable the short W–W distance is in these compounds. exactly at the crossing of the W–W COOP from bonding to ˚ ˚ It is down to 2.08 A in one case, up to 2.37 A in another, antibonding, and not far from that crossing in Ca2W6O8 .In but mostly stays in the quadruple bond range of 2.20–2.30 A˚ . the latter compound there is some electron transfer from the 4 4 4 2þ The shortest WW bond is obtained for 88 electrons, the d –d W6O8 sublattice to the Ca sublattice; this moves the Fermi system. There is no correlation of WW distances with the lat- level into the d region of the metal oxide sublattice. A crystal tice constant. We take the computed geometries as an indica- orbital Hamilton population (COHP) analysis of the DFT tion that these systems should be stable. All systems turn out calculation on Ca2W6O8 leads to the same conclusion. 4 to be metallic in the DFT calculations, except W6E8 , E ¼ O, S, and W O F (no A atom in these cases). 6 4 4 Band structure Our parallel efforts to reparameterize the eH method, driven by the multitude of analytical tools available within this The band structure of Ca2W6O8 is shown in Fig. 4 together method, focused on a still more hypothetical (countercation- with the DOS. Ca2W6O8 turns out to be metallic. From the 4 free) W6O8 and Ca2W6O8 . A change of 2 eV in the Hii of DOS in Fig. 4 we see that the whole region around the Fermi W 5d, and a small adjustment in the diffuseness of the W 5d level is made up from W d electrons, with a small admixture of orbital (the final eH parameters are given in the Theoretical O p electrons. There is a pseudo-gap at about E ¼1.4 eV. 4 methods section) gave band structures for W6O8 similar Interestingly, the DOS shows several pronounced peaks, for to the DFT results. Some further small variation in the example one at 1.9 eV below the Fermi level. This peak

Table 1 Computed crystal structure data for A2W6E8 compounds. Ne : number of electrons in the formula unit; a is the lattice constant; xW : x coordinate of the W atom; yE1 : y coordinate of the E1 atom; yE2 : y coordinate of the E2 atom (only for structures with two kinds of anions E); dW–W : W–W bond distance; dW–E1 : W–E1 bond distance; dW–E2 : W–E2 bond distance; dA1–E : distance A1 (at corner of the unit cell) to E; ˚ dA2–E : distance A2 (at center of the unit cell) to E. All distances are in A.

Composition Space group Ne axW yE1 yE2 dW–W dW–E1 dW–E2 dA1–E dA2–E

4 W6O8 Pm-3 88 6.513 0.330 0.265 – 2.22 2.35 – 2.65 2.99 4 W6S8 Pm-3 88 7.486 0.351 0.267 – 2.23 2.73 – 3.02 3.47 W6S4P4 P23 80 6.743 0.329 0.257 0.741 2.31 2.43 2.43 – – W6O4Cl4 P23 88 6.168 0.322 0.277 0.799 2.19 2.21 2.35 – – W6O4N4 P23 80 5.698 0.292 0.259 0.755 2.37 2.03 2.03 – – W6O4F4 P23 88 5.878 0.316 0.262 0.731 2.16 2.11 2.10 – – W6S4Cl4 P23 88 6.776 0.337 0.257 0.737 2.20 2.46 2.45 – – W6Cl8 Pm-3 92 6.837 0.337 0.259 – 2.22 2.48 – – – W6S8 Pm-3 84 6.719 0.331 0.260 – 2.28 2.42 – – – Ca2W6S8 Pm-3 88 6.818 0.337 0.253 – 2.22 2.48 – 2.99 2.91 Mg2W6S8 Pm-3 88 6.765 0.337 0.252 – 2.21 2.46 – 2.95 2.91 K2W6S8 Pm-3 86 6.865 0.336 0.257 – 2.26 2.49 – 3.05 2.89 W6O8 Pm-3 84 5.725 0.304 0.254 – 2.24 2.04 – – – W6F8 Pm-3 92 6.034 0.327 0.233 – 2.08 2.21 – – – Be2W6O8 Pm-3 88 5.668 0.303 0.214 – 2.24 2.09 – 2.10 2.81 Mg2W6O8 Pm 3 88 5.780 0.307 0.225 – 2.23 2.11 – 2.25 2.75 Ca2W6O8 Pm 3 88 5.879 0.307 0.251 – 2.27 2.10 – 2.56 2.53 Zn2W6O8 Pm 3 88 5.777 0.307 0.225 – 2.23 2.11 – 2.25 2.75

This journal is Q The Royal Society of Chemistry and the 186 New. J. Chem., 2004, 28, 185–190 Centre National de la Recherche Scientifique 2004 6 12 Fig. 2 Interaction of two WO4 (C4v) fragments, resulting in W2O8 (D4h). The energies are obtained from eH calculations. The major contributions to the MOs are indicated.

4 Fig. 3 Crystal orbital overlap population (COOP) between W–W in (a) Ca2W6O8 and (b) W6O8 as computed from eH calculations. Positive COOP indicates bonding.

This journal is Q The Royal Society of Chemistry and the New. J. Chem., 2004, 28, 185–190 187 Centre National de la Recherche Scientifique 2004 Fig. 4 Band structure of Ca2W6O8 along lines of high symmetry in the Brillouin zone (left) and corresponding density of states (DOS; computed using a 13 13 13 mesh, right). Note that we used the unconventional Z point instead of the symmetry equivalent X point. The full DOS is given by the black curve. Dark grey, medium grey and light grey ﬁlled areas show W, O, and Ca site projections of the DOS.

originates from an extremely flat band in the band structure, reaction (at p ¼ 0 Pa and T ¼ 0 K). For example, Ca2W6O8 following the path from G to Z. may decompose according to the reaction: The Z point we use is symmetrically equivalent to the X point (so is the path G–Z to G–X). Usage of Z, however, allows Ca2W6O8 ! 2CaWO4 þ 4W the interpretation of the s, p, and d bands using the standard d We calculated the compounds on the right side of this orbitals on W. On doing so, the flat band between G and Z can 2 reaction, scheelite and tungsten, applying the same computa- be recognized as the d band arising from dx2 y and dxy orbi- tional procedure as for Ca2W6O8 . The enthalpy difference tals on W. Steep bands are also observed, for example, the calculated in this way was found to be 8 eV (0.5 eV per band that crosses the Fermi level between G and Z, which is atom). the s band, predominantly of dz2 character. The simultaneous Admittedly, this is a pretty large driving force for decompo- presence of steep and extremely flat band portions around the sition. There are, however, several synthetic strategies avail- Fermi level has been suggested to be a ‘‘fingerprint’’ for a 11 able to synthesize comparable metastable structures, such as potentially superconducting compound. The structural rela- epitaxy or template synthesis. We, therefore, think that the tion to the superconducting phases of Nb3Ge and Nb3Sn men- local minimum of this unusual structure can be attained, if tioned above becomes interesting in this context. One might not for Ca W O , then for some other realization. think about removing some electrons from this material by 2 6 8 the usual chemical stratagems, so as to bring the flat band closer to the Fermi level. Computed COHP curves are provided in Fig. 5. The region Other structures with multiple metal-metal bonding from 10 eV to 5 eV is Ca–O and W–O bonding. The region The construction principle we applied to generate the from 5eVto1.6 eV is strongly W–W bonding. This strong Ca2W6O8 structure from the CaF2 type may be applied to gen- bonding apparently dominates the structure and provides erate other potential extended structures with strongly bonded much of the cohesive energy of the system. The W–W COHP MM dumbbells in them. One just looks for simple structural curve switches from bonding to antibonding just at the Fermi types with at least one eight-coordinated cation, and proceeds level. to ‘‘split’’ that cation into an MM pair. For example, we may take the CsCl structure type (both Cs and Cl eight-coordinated). By splitting the central position, we come to W2X (X any kind of anion). To make W formally 2þ, X would be Energetics C with a 4 formal charge. The structure of Ca2W6O8 is mechanically stable against dis- Another opportunity is offered up by the Th3P4 structure tortions of its structural parameters. In this sense, Ca2W6O8 type. If we split the one Th position into an M–M pair, we constitutes a local energy minimum on the multi-dimensional end up with M3E2 , possibly quadruply bonded for M ¼ W, potential energy surface for this particular composition. How E ¼ N.12 This formal type of crystal engineering is illustrated stable, however, might it be thermodynamically? We compared in Fig. 6. Interestingly, the structure we created in this way is the energy of Ca2W6O8 with the energies of its likely decompo- already known in solid state chemistry, it is the anti-type of 13 sition products, that is the enthalpy of a decomposition the La2C3 structure.

This journal is Q The Royal Society of Chemistry and the 188 New. J. Chem., 2004, 28, 185–190 Centre National de la Recherche Scientifique 2004 Fig. 5 COHP curves in Ca2W6O8 . Note that we plot COHP, therefore, positive values (on right side of each graph) indicate bonding, negative values indicate antibonding.

12 In a model calculation on W2O8 , the D2d geometry at C2 , z1 and z2 are the coefficients and exponents in a double-z right in Fig. 6 is destabilized (the e p levels go up in energy) expansion of the 5d Slater orbital. 16 relative to a D4h structure. But the essential features of quad- For density functional calculations we applied the VASP ruple bonding are retained. Exploring structural stability software.17 This implementation of DFT methods combines by geometry optimization, a preliminary calculation on W3N2 a plane-wave basis set with the total energy pseudopotential leads (after much relaxation) to a 3-connected net (with W–W approach. The pseudopotentials employed are based on the bonds). There are, however, still some large interstitial sites in projector-augmented-wave (PAW) method.18 We used both this structure that could be filled with suitable atoms. More- the local density approximation (LDA) and the generalized- over, not all Th positions need to be split (there are 12 of them gradient approximation (GGA) to treat the exchange-correla- in the conventional unit cell of Th3P4). tion energy of the electrons. All results rely on well-converged Finally, we note that a variety of further structural types structures with respect to cut-off energy (500 eV) and k point may be derived from the A2M6E8 structure, by rotating the sampling (4 4 4 mesh). Residual forces and stresses in the MM dumbbells. One highly symmetric variant (space group optimized structures are below 0.01 eV A˚ 1 and 1 kbar, Pm-3m, Fig. 7), for instance, may be obtained by orienting respectively. the dumbbells so that they all ‘‘point’’ at the central site. This We tested different kinds of pseudopotentials for Ca and W. structure has already been studied theoretically, as a cubic In the case of Ca, we detected no significant difference whether alternative to the Chevrel phases.14 the 3p electrons were treated either as core or valence states. There’s clearly a large playground awaiting theoretical and experimental children here.

Theoretical methods Extended Hu¨ckel calculations were carried out using the 15 YAeHMOP program and parameters listed in Table 2. C1 ,

Fig. 6 A way of building up an MM multiply bonded structure by splitting of the Th position in the Th3P4 structure type. The regular Fig. 7 A variant of the A2M6X8 structure with higher (Pm-3m) ThP8 bisdisphenoid is transformed into an M2E8 unit. symmetry.

This journal is Q The Royal Society of Chemistry and the New. J. Chem., 2004, 28, 185–190 189 Centre National de la Recherche Scientifique 2004 Table 2 Extended Hu¨ckel parameters 5(a)J.Ko¨hler and A. Simon, Angew. Chem., Int. Ed. Engl., 1986, 25, 996; (b) S. J. Hibble, A. K. Cheetham and D. F. Cox, Inorg.

z1 Hii/eV C1 z2 C2 Chem., 1987, 26, 2389; (c) P. Alemany, V. G. Zubkov, S. Alvarez, V. P. Zhukov, V. A. Pereliaev, I. Kontsevaya and A. Tyutyunnik, Ca 4s 1.200 7.00 J. Solid State Chem., 1993, 105, 27; (d ) B. Harbrecht and A. Ritter, Z. Anorg. Allg. Chem., 1999, 625, 178. Ca 4p 1.200 4.00 6 For some strategies for linking large arrays of multiply-bonded O 2s 2.275 32.30 MM units, see: (a) M. H. Chisholm, J. Organomet. Chem., O 2p 2.275 14.80 2002, 641, 12; (b) F. A. Cotton, C. Lin and C. A. Murillo, Proc. W 6s 2.340 8.26 Natl. Acad. Sci. U.S.A., 2002, 99, 4810. W 6p 2.309 5.17 7 M. J. Bucknum, Chemistry Preprint Server (CPS), 2002, W 5d 4.782 13.37 0.6685 1.860 0.5424 physchem/0204007. 8 For leading references see: K. B. Schwartz, C. T. Prewitt, R. D. Shannon, L. M. Corliss, J. M. Hastings and B. L. Chamberland, Acta Crystallogr. Sect. B, 1982, 38, 363; D. A. Keszler and J. A. For W the particular choice of pseudopotential employed Ibers, Inorg. Chem., 1983, 22, 3367; M. Wakeshima, T. Fujino, (defining the 5p electrons as core or valence) had no effect N. Sato, K. Yamada and H. Matsuda, J. Solid State Chem., on the W–O bond length, but influenced the W–W bond 1997, 129,1. length. Unless stated otherwise, all results reported were 9(a)J.Mu¨ller, Rep. Prog. Phys., 1980, 43, 641; L. R. Testardi, obtained within the GGA with pseudopotentials that have Rev. Mod. Phys., 1975, 47, 637; (b) Though it’s an important the p electrons defined as core states. and interesting topic, a detailed investigation of this Peierls distortion is out of place here. In addition we used the TB-LMTO method to analyze the 19 10 A. R. Chakravarty, F. A. Cotton and E. S. Shamshoum, electronic structure in more detail. Band structure, density Inorg. Chem., 1984, 23, 4216. of states (DOS) and the crystal orbital Hamilton population 11 A. Simon, Angew. Chem., Int. Ed. Engl., 1997, 36, 1788. 20 (COHP) were investigated within the LDA. The LMTO 12 More precisely, here is what was done: Th3P4 is in space group ˚ calculations are done for geometries first optimized within I-43d. The cell constant was chosen as a ¼ 8.6 A. The Th are at the plane-wave method. 12a (3/8 0 1/4), P at 16c (xxx), with x ¼ 1/12, which makes all Th–P distances equal, Th–P ¼ 2.977 A˚ (for a ¼ 8.6 A˚ ). The Th position at 12a was then split into two. It becomes 24d. There is now a new free parameter, the x position of the cation (Th or Acknowledgements W). It will determine the bond distance W–W. In the new structure the atom positions are as follows: W 24d [x(W) 0 1/4]; choose We are grateful to the National Science Foundation for its x(W) ¼ 0.25 for W–W ¼ 2.15 A˚ ,N16c (xxx); choose support of this research through grant CHE-0204841. x ¼ 0.0417 to have four equal bond distances W–N ¼ 2.559 A˚ . 13 M. Atoji, K. A. Gschneidner, A. H. Daane, R. E. Rundle and F. H. Spedding, J. Am. Chem. Soc., 1958, 80, 1804. 14 T. Hughbanks, Inorg. Chem., 1986, 25, 1492. References 15 G. A. Landrum and W. V. Glassey, YAeHMOP: Yet Another Extended Hu¨ckel Molecular Orbital Package,version 3.0.2. 1 F. A. Cotton and R. A. Walton, Multiple Bonds between Metal The YAeHMOP software is freely available on the web at http:// Atoms, Oxford, New York, 1993. sourceforge.net/projects/yaehmop/. 2(a) W. Jeitschko, D. H. Heumannska¨mper, M. S. Schriewer- 16 P. Hohenberg and W. Kohn, Phys. Rev. A, 1964, 136, 864. Po¨ttgen and U. Ch. Rodewald, J. Solid State Chem., 1999, 147, 17 (a) G. Kresse and J. Hafner, Phys. Rev. B, 1993, 47, 558; (b)G. 218; (b) K. Waltersson, Acta Crystallogr, Sect. B., 1976, 32, Kresse and J. Hafner, Phys. Rev. B, 1994, 49, 14 251; (c) G. Kresse 1485; (c) J.-P. Besse, G. Baud, R. Chevalier and M. Gasperin, and J. Furthmu¨ller, Comput. Mater. Sci., 1996, 6, 15. Acta Crystallogr., Sect. B, 1978, 34, 3532; (d ) G. Wltschek, H. 18 G. Kresse and D. Joubert, Phys. Rev. B, 1999, 59, 1758. Paulus, H. Ehrenberg and H. Fuess, J. Solid State Chem., 1997, 19 O. K. Andersen and O. Jepsen, The Stuttgart TB-LMTO-ASA 132, 196. Program, version 47, MPI fu¨r Festko¨rperforschung, Stuttgart, 3 O. Hochrein, Y. Grin and R. Kniep, Angew. Chem., Int. Ed., 1998, Germany, 2000. Available under http://www.mpi-stuttgart. 37, 1582. mpg.de/andersen. 4 M. S. Bailey, M. N. Obrovac, E. Baillet, T. K. Reynolds, D. B. 20 R. Dronskowski and P. E. Blo¨chl, J. Phys. Chem., 1993, 97, Zax and F. J. DiSalvo, Inorg. Chem., 2003, 42, 5572. 8617.

This journal is Q The Royal Society of Chemistry and the 190 New. J. Chem., 2004, 28, 185–190 Centre National de la Recherche Scientifique 2004